Use of a Simple Mechanical Analogy to Analytically Tune the PD Controller of a Flexible Manipulator System

Abstract

A study is presented in this paper that uses a simple mechanical analogy to analytically tune the PD (proportional-derivative) controller of a linear flexible manipulator system. More specifically, the aim is to give simple closed-form solutions of the optimal P and D gains to yield the maximum bandwidth under a given damping requirement or conversely the maximum damping under a given bandwidth requirement. The idea of this study is based on the observation that the performance of the complete manipulator system is largely determined by the operational dynamics of the fundamental vibration mode. A lumped element method is thus applied to model this dynamics in terms of simple lumped mechanical elements. It subsequently turns out that the original servo control problem is analogous to a conventional Zener mount design problem, that is, mathematically, to optimize a third-order dynamic system consisting of the Zener model of a viscoelastic mount and an inertial object upon it. A design methodology is finally established to analytically determine the optimal elements of the mount, corresponding to the optimal control gains. Simulations and experiments were also conducted with a single-link flexible beam to support the model and the design methodology developed.

Intelligent Manipulator with Flexible Link and Joint: Modeling and Vibration Control

“…Furthermore, manipulators with two or more links were also analyzed employing the FE method [20,21]. An important purpose of dynamical analysis of flexible manipulators is to suppress the vibration of flexible structures [22,23]. Many studies showed that the control schemes were effective for vibration control of flexible manipulators.…”

New development of the dynamic modeling and the inverse dynamic analysis for flexible robot

“…It can be seen that, in recent years, though there have been several studies related to the flexible manipulators, a few attempts focus on the inverse dynamic analysis for the flexible robots, especially the flexible robots with the translational joints. Most of the works only take into account the revolute joints [17][18][19][20][21][22][23][24][25][26][27][28] when considering the dynamic modeling and analysis of a flexible robot. The large deformation of a flexible link was studied by Celentano.…”

“…[18][19][20]23 Also, the control issues were addressed in the recent works. [24][25][26][27][28] In the literature, the inverse dynamic analysis for flexible robots has been studied by a number of authors. Kwon and Book 29 used AMM for the modeling of the linear inverse dynamics of a single flexible link robot with one rotational joint.…”

Dynamic Modeling and Development of Symbolic Calculation Software for N‐DOF Flexible‐Link Manipulators Incorporating Lumped Mass

“…Robotic manipulators are widely used in environments that are hazardous to humans and in situations where there are substantial amounts of repetitive work to reduce the burden on humans and to assist in accomplishing special tasks. To ensure sufficient positioning accuracy at the end of a manipulator, the links of the manipulator can generally be stiffened by a bulky structure to prevent the links from vibrating and to avoid elastic deflection during operation [1][2][3][4]. However, heavy links limit the speed of the manipulator's movement and consume excessive amounts of energy.…”